On Steepest-Descent-Kaczmarz methods for regularizing systems of nonlinear ill-posed equations

We investigate modified steepest-descent methods coupled with a loping Kaczmarz strategy for obtaining stable solutions of nonlinear systems of ill-posed operator equations. We show that the proposed method is a convergent regularization method. Numerical tests are presented for a linear problem related to photoacoustic tomography and a nonlinear problem related to the testing of semiconductor devices.